The bottom of the ladder is 5 feet tall from the wall. the ladder is 13 feet long. about how high is the wall?
Time for the Pythagorean theorem since you're looking at a right-angle triangle.
a^2 + b^2 = c^2
5^2 + b^2 = 13^2
25 + b^2 = 169
b^2 = 169 - 25
b^2 = 144
b = 12
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To determine the height of the wall, we can use the Pythagorean Theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).
In this case, the ladder is the hypotenuse, and the distance from the bottom of the ladder to the wall is one of the sides. Let's assume this distance is represented by 'a'. The height of the wall is the other side, which we'll call 'b'.
Using the Pythagorean Theorem:
a^2 + b^2 = c^2
Substituting the given values into the equation:
5^2 + b^2 = 13^2
25 + b^2 = 169
b^2 = 169 - 25
b^2 = 144
Taking the square root of both sides:
b = sqrt(144)
b = 12
Therefore, the height of the wall is approximately 12 feet.